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| 1 | #include<stdio.h> | |
| 2 | #include<stdlib.h> | |
| 3 | ||
| 4 | #define bool int | |
| 5 | ||
| 6 | /* A binary tree node has data, pointer to left child | |
| 7 | and a pointer to right child */ | |
| 8 | struct node | |
| 9 | {
| |
| 10 | int data; | |
| 11 | struct node* left; | |
| 12 | struct node* right; | |
| 13 | }; | |
| 14 | ||
| 15 | /* | |
| 16 | Original example code. | |
| 17 | ||
| 18 | Given a tree and a sum, return true if there is a path from the root | |
| 19 | down to a leaf, such that adding up all the values along the path | |
| 20 | equals the given sum. | |
| 21 | ||
| 22 | Strategy: subtract the node value from the sum when recurring down, | |
| 23 | and check to see if the sum is 0 when you run out of tree. | |
| 24 | */ | |
| 25 | bool hasPathSum_original(struct node* node, int sum) | |
| 26 | {
| |
| 27 | /* return true if we run out of tree and sum==0 */ | |
| 28 | if (node == NULL) | |
| 29 | {
| |
| 30 | return (sum == 0); | |
| 31 | } | |
| 32 | ||
| 33 | else | |
| 34 | {
| |
| 35 | bool ans = 0; | |
| 36 | ||
| 37 | /* otherwise check both subtrees */ | |
| 38 | int subSum = sum - node->data; | |
| 39 | ||
| 40 | /* If we reach a leaf node and sum becomes 0 then return true*/ | |
| 41 | if ( subSum == 0 && node->left == NULL && node->right == NULL ) | |
| 42 | return 1; | |
| 43 | ||
| 44 | if(node->left) | |
| 45 | ans = ans || hasPathSum_original(node->left, subSum); | |
| 46 | if(node->right) | |
| 47 | ans = ans || hasPathSum_original(node->right, subSum); | |
| 48 | ||
| 49 | return ans; | |
| 50 | } | |
| 51 | } | |
| 52 | ||
| 53 | /* | |
| 54 | - | Here is the original example without optimization. You'll see that the algorithm is much cleaner now. You had a bug in your rewrite as it answered the question "Is there A path with the given sum?" when you had nodes which had a left node without a right one (or vice versa). |
| 54 | + | Here is the original example without optimization. You'll see that the algorithm is much cleaner now. |
| 55 | Note that this will short-circuit the calls in the line with the return statement. | |
| 56 | */ | |
| 57 | bool hasPathSum_revised(struct node* node, int sum) | |
| 58 | {
| |
| 59 | /* return true if we run out of tree and sum==0 */ | |
| 60 | if (node == NULL) | |
| 61 | return (sum == 0); | |
| 62 | ||
| 63 | /* otherwise check both subtrees */ | |
| 64 | int subSum = sum - node->data; | |
| 65 | return hasPathSum_revised(node->left, subSum) || hasPathSum_revised(node->right, subSum); | |
| 66 | } | |
| 67 | ||
| 68 | /* | |
| 69 | Find the minimum in the binary tree - without making any assumptions. | |
| 70 | Call this with an "impossible" minimum at top level. | |
| 71 | */ | |
| 72 | int findMin(struct node* node, int min) {
| |
| 73 | if (!node) return min; | |
| 74 | if (node->data < min) | |
| 75 | min = node->data; | |
| 76 | ||
| 77 | int leftMin = findMin(node->left, min); | |
| 78 | if(leftMin < min) | |
| 79 | min = leftMin; | |
| 80 | ||
| 81 | int rightMin = findMin(node->right, min); | |
| 82 | if(rightMin < min) | |
| 83 | min = rightMin; | |
| 84 | ||
| 85 | return min; | |
| 86 | } | |
| 87 | ||
| 88 | /* UTILITY FUNCTIONS */ | |
| 89 | /* Helper function that allocates a new node with the | |
| 90 | given data and NULL left and right pointers. */ | |
| 91 | struct node* newnode(int data) | |
| 92 | {
| |
| 93 | struct node* node = (struct node*) | |
| 94 | malloc(sizeof(struct node)); | |
| 95 | node->data = data; | |
| 96 | node->left = NULL; | |
| 97 | node->right = NULL; | |
| 98 | ||
| 99 | return(node); | |
| 100 | } | |
| 101 | ||
| 102 | void freetree(struct node* node) | |
| 103 | {
| |
| 104 | if(!node) | |
| 105 | return; | |
| 106 | freetree(node->left); | |
| 107 | freetree(node->right); | |
| 108 | free(node); | |
| 109 | } | |
| 110 | ||
| 111 | /* Generate a random full binary tree where every path to a leaf has the | |
| 112 | totalsum given */ | |
| 113 | struct node* generatetree(struct node* node, unsigned depth, int totalsum) {
| |
| 114 | if(depth == 0) {
| |
| 115 | node->data = totalsum; | |
| 116 | return node; | |
| 117 | } | |
| 118 | node->data = (rand() % 100) - 50; | |
| 119 | node->left = newnode(0); | |
| 120 | node->right = newnode(0); | |
| 121 | generatetree(node->left, depth-1, totalsum - node->data); | |
| 122 | generatetree(node->right, depth-1, totalsum - node->data); | |
| 123 | return node; | |
| 124 | } | |
| 125 | ||
| 126 | void inspecttree(struct node* root, int expected_sum) {
| |
| 127 | printf("Original:\n");
| |
| 128 | if(hasPathSum_original(root, expected_sum)) | |
| 129 | printf("There is a root-to-leaf path with sum %d\n", expected_sum);
| |
| 130 | else | |
| 131 | printf("There is no root-to-leaf path with sum %d\n", expected_sum);
| |
| 132 | ||
| 133 | printf("Revised:\n");
| |
| 134 | if(hasPathSum_revised(root, expected_sum)) | |
| 135 | printf("There is a root-to-leaf path with sum %d\n", expected_sum);
| |
| 136 | else | |
| 137 | printf("There is no root-to-leaf path with sum %d\n", expected_sum);
| |
| 138 | /* where was INT_MAX defined again :( */ | |
| 139 | printf("Minimum: %d\n", findMin(root, 60000));
| |
| 140 | } | |
| 141 | ||
| 142 | /* Driver program to test above functions*/ | |
| 143 | int main() | |
| 144 | {
| |
| 145 | srand(time(NULL)); | |
| 146 | int sum = 21; | |
| 147 | ||
| 148 | /* Hand constructed binary tree is | |
| 149 | 10 | |
| 150 | / \ | |
| 151 | 8 2 | |
| 152 | / \ / | |
| 153 | 3 5 2 | |
| 154 | */ | |
| 155 | struct node *root = newnode(10); | |
| 156 | root->left = newnode(8); | |
| 157 | root->right = newnode(2); | |
| 158 | root->left->left = newnode(3); | |
| 159 | root->left->right = newnode(5); | |
| 160 | root->right->left = newnode(2); | |
| 161 | inspecttree(root, sum); | |
| 162 | freetree(root); | |
| 163 | ||
| 164 | root = generatetree(newnode(0), 8, 1000); | |
| 165 | inspecttree(root, 1000); | |
| 166 | freetree(root); | |
| 167 | ||
| 168 | getchar(); | |
| 169 | return 0; | |
| 170 | } |